Strukturaussagen für die optimalen Ausübungsstrategien bei multiplen Stoppproblemen und Swing Optionen

This thesis is concerned with the following stochastic dynamic optimization problem.
A decision maker, who maximizes his expected utility, is supposed to consume a
given capacity under constraints in a finite time horizon. At each point of time there
is an offer and the decision maker receives a reward, which depends on the value of
the offer and the consumed quantity. The aim is to maximize the expected utility
of the total reward. In this context multiple optimal stopping problems as well as
swing options, which are important in the energy sector, are investigated.
The decision problem is considered for linear and exponential utility functi
ons using the theory of Markov Decision Processes. For a risk-neutral decision ma
ker with a linear utility function we give conditions for the sequence of offers that
guarantee the existence of thresholds. Furthermore, we study the behaviour of the
thresholds when the planning horizon tends to infinity. In the case of a risk-averse
decision maker with an exponential utility function the solution is different. The
boundary points of the admissible set are in general no longer optimal. Additional
ly, we investigate how attitude to risk affects the optimal strategy. The results are
illustrated by several examples.